Exercise 7.4 Archives - Noon Academy

Exercise 7.4

The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC.
(i) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1
(ii) What are the coordinates of the centroid of the triangle ABC?

CBSE, Class 10, Coordinate Geometry, Exercise 7.4, Maths, NCERT Exemplar

Solution: (i) Let (p, q) be the coordinates of a point Q. Provided, The point Q (p, q), Divide the line joining $\mathrm{B}\left(\mathrm{x}{2}, \mathrm{y}{2}\right)$ and...

The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC. (i) The median from A meets BC at D. Find the coordinates of the point D. (ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1

CBSE, Class 10, Coordinate Geometry, Exercise 7.4, Maths, NCERT Exemplar

Solution: According to the given question, A, B and C are the vertices of ΔABC A(x1, y1), B(x2, y2), C(x3, y3) are the coordinates of A, B and C. (i) According to the information provided, D is BC's...

A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of △ ADE.

CBSE, Class 10, Coordinate Geometry, Exercise 7.4, Maths, NCERT Exemplar

Solution: According to the given question, A (6, 1), B (8, 2) and C (9, 4) are the three vertices of a parallelogram ABCD Let (x, y) be the fourth vertex of parallelogram. It is known to us that,...

If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

CBSE, Class 10, Coordinate Geometry, Exercise 7.4, Maths, NCERT Exemplar

Solution: Let (x,y) be the vertices. The distance between (x,y) & (4,3) is $=\text{ }\surd ({{\left( x-4 \right)}^{2}}~+\text{ }{{\left( y-3 \right)}^{2}})$……(1) The distance between (x,y) &...

The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC.
(i) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1
(ii) What are the coordinates of the centroid of the triangle ABC?

The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC. (i) The median from A meets BC at D. Find the coordinates of the point D. (ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1

A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of △ ADE.

If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

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The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC. (i) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1 (ii) What are the coordinates of the centroid of the triangle ABC?

The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC. (i) The median from A meets BC at D. Find the coordinates of the point D. (ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1

A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of △ ADE.

If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

The points A (x1, y1), B (x2, y2) and C (x3 y3) are the vertices of ABC.
(i) Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1
(ii) What are the coordinates of the centroid of the triangle ABC?